1. Field of the Invention
Example embodiments relate generally to downlink scheduling of users in a multi-user, multiple-input and multiple-output (MU-MIMO) system. Pre-selection of a subset of users, for purposes of the scheduling, may be accomplished without first obtaining channel state information for each of the users.
2. Related Art
The next generation of wireless communication systems (e.g., 802.16m, LTE-Advanced, etc.) use multi-user MIMO (MU-MIMO) as a core technology. A considerable research effort has been dedicated to the performance evaluation of MU-MIMO systems under realistic cellular environments. In a MU-MIMO system, Inter-Cell Interference (ICI) may be treated as noise which may significantly limit system capacity. Using a network MIMO approach, clusters of cooperating base stations (BSs) act as a single distributed MIMO transmitter and interference from other clusters of BSs is treated as noise. Each cluster seeks to maximize its own objective function defined by fairness scheduling.
FIG. 1 is a simplified diagram of conventional clusters of base stations 110 (see clusters 1 through L). Specifically, each cluster may include a number of base stations 110, numbered 1 through B. Each cluster may include a central cluster controller 120 with a central scheduling unit 125. The central scheduling unit 125 may be instrumental in ensuring that the base stations 1-B of each cluster “cooperate,” from the standpoint that each cluster of base stations 1-B act as a single distributed MIMO transmitter that seeks to maximize its own objective function (which may maximize transmitter output while reducing interference from other clusters).
FIG. 2 is an exemplary diagram of a single conventional cluster of base stations 110. Specifically, FIG. 2 includes a cluster with two base stations 110 (BS1, and B52), though more than two base stations 100 may be included per cluster. In this example, both base stations 110 serve two cells (cell 1, and cell 2), though other clusters may include different numbers of cells. Within each cluster there may be K collocated user groups (for instance, as shown in FIG. 2, we assume that user groups 1-4 belong to cell 1 of the cluster, and groups 5-8 belong to cell 2 of the cluster). The users in the same group are “collocated,” from the standpoint that the users experience the same path loss (and, have the same path loss coefficients) from the base station while their small scale fading channel coefficients are independent and identically distributed (i.i.d), as the user equipment included within the group is in a similar physical location.
FIG. 3 is a simplified diagram of a conventional base station 110 including multiple antennas 135 (antenna 1 through antenna γN). Transmissions from the multiple antennas 135 may be accomplished via a base station scheduling unit 140. The base station 110 may transmit to K user groups 130, each user group potentially including multiple user equipment 145 (1-N), and each user equipment including an antenna 150. At any instance of time, each antenna 145 may transmit to only a single user equipment 145, creating a limit in transmission capacity for the cluster.
Based on the general understanding of FIGS. 1-3, as described above, a more mathematical description of the system of FIGS. 1-3 in now included herein. At the outset, it should be understood that user in a same group 130 (as shown in FIGS. 2-3) are statistically equivalent. In other words, they see the same pathloss coefficients from all BSs, and their small-scale fading channel coefficients are independently and identically distributed. The received signal vector yk=[yk,1 . . . yk,N]TεCN for the k-th user group is given by:
                              y          k                =                                            ∑                              m                =                1                            M                        ⁢                                          α                                  m                  ,                  k                                            ⁢                              H                                  m                  ,                  k                                H                            ⁢                              x                m                                              +                      n            k                                              (        1        )            
Symbols αmk and Hm,k may denote the distance dependent pathloss coefficient and γN×N small-scale channel fading matrix from the m-th BS to the k-th user group, respectively, xm=[xm,1 . . . xm,γN]TεCγN is the transmitted signal vector of the m-th BS, subject to the power constraint tr(Cov(xm))≦Pm, and nk=[nk,1 . . . nk,N]TεCN denotes the additive white Gaussian noise (AWGN) at the user receivers. The elements of nk and of Hm,k are independently and identically distributed.
A cooperative cell arrangement with L cooperation clusters is defined by the BS partition {M1, . . . , ML} of the BS set {1, . . . , M} and the corresponding user group partition {K1, . . . , KL} of the user group set {1, . . . , K}. It is assumed that the BSs 110 in each cluster Ml act as a single distributed multi-antenna transmitter with γ|Ml|N antennas, perfectly coordinated by a central cluster controller, and serving users in groups kεKl. The clusters do not cooperate, as each cluster treats ICI from other clusters as noise. Assuming that each BS operates at its maximum individual transmit power, the ICI plus noise power at any user terminal in group kεKl is given by:
                              σ          k          2                =                  1          +                                    ∑                              m                ∉                                  M                  l                                                      ⁢                                          α                                  m                  ,                  k                                2                            ⁢                                                P                  m                                .                                                                        (        2        )            
Each cluster seeks to maximize its own objective function defined by fairness scheduling. Under the above system assumptions, a selfish optimal strategy that operates at maximum per-BS power is a Nash equilibrium of the system. At this Nash equilibrium, the clusters are effectively decoupled since the effect that other clusters have on each cluster l is captured by the ICI terms in (2) that do not depend on the actual BS transmit covariances Cov(xm).
From the viewpoint of cluster l, the system is equivalent to a single-cell MIMO downlink channel with a modified channel matrix and noise levels and a per-BS power constraint. Therefore, for a given reference cluster l=1, the user groups in the reference cluster may be indicated as k=1, . . . , A, with A=|K1|, and the BSs in M1 as m=1, . . . , B with B=|M1|. After a convenient re-normalization of the channel coefficients, we arrive at the equivalent channel model for the reference cluster given by:y=HHx+z  (3)with yε CAN, xε CγBN, z˜CN(0, IAN) and the channel matrix HεCγBN×AN is given by
                              H          =                      [                                                                                                      β                                              1                        ,                        1                                                              ⁢                                          H                                              1                        ,                        1                                                                                                              …                                                                                            β                                              1                        ,                        A                                                              ⁢                                          H                                              1                        ,                        A                                                                                                                                          ⋮                                                                                                                                          ⋮                                                                                                                        β                                              B                        ,                        1                                                              ⁢                                          H                                              B                        ,                        1                                                                                                              …                                                                                            β                                              B                        ,                        A                                                              ⁢                                          H                                              B                        ,                        A                                                                                                                  ]                          ,                            (        4        )                            where we define βm,k=αm,k/σk         
The pathloss coefficients are fixed constants that depend only on the geometry of the system. The small-scale fading coefficients are assumed to change independently from time slot to time slot according to a classical block-fading model (noting that a “time slot” indicates a number of channel uses over which the small-scale coefficients can be considered constant, which is approximately equal to the product of channel coherence time and the channel coherence bandwidth). This is representative of a typical scenario where the distance between BSs and users changes significantly over a time-scale of the order of the tens of seconds (due to movement of the users), while the small-scale fading decorrelates completely within a few milliseconds.
Referring to FIG. 1, the cluster controller 120 including a central controller 120 that operates according to a downlink scheduling scheme that allocates instantaneously the transmission resource (signal dimensions and transmit power) to the users. To accomplish this, we focus on the weighted instanteneous sum-rate maximization problem:
                              maximize          ⁢                                          ⁢                                    ∑                              k                =                1                            A                        ⁢                                          ∑                                  i                  =                  1                                N                            ⁢                                                W                  k                                      (                    i                    )                                                  ⁢                                  R                  k                                      (                    i                    )                                                                                      ⁢                                  ⁢                              subject            ⁢                                                  ⁢            to            ⁢                                                  ⁢            R                    ∈                                    R              lzfb                        ⁡                          (              H              )                                                          (        5        )            
Symbol Wk(i) denotes the rate weight for user i in group k, and Rlzfb(H) is the achievable “instantaneous” rate region of Linear Zero-Forcing Beamforming (LZFB) for given channel matrix H. It should be understood that “instantaneous” means that this rate region depends on the given channel realization H, in contrast with the throughput region R, that depends on the statistics of H. It is assumed that A≧γB (i.e., with reference to FIG. 3, the number of users 145 in the cluster is larger than the total number of base station antennas 135 in the cluster) and that all coefficients βm,k are strictly positive. Therefore, rank(H)=γBN is satisfied. In this case, LZFB cannot serve simultaneously all users in the cluster, and the scheduler must select a subset of users not larger than γBN, to be served at each time slot. The solution of (5) is generally difficult, since it requires: 1) a search over all user subsets of cardinality less or equal to γBN, and 2) either a full or a large amount of CSIT (Channel State Information at the Transmitter) feedback since it needs CSIT reports from many (or, all) users in order to select a subset of users at each scheduling slot, even though no more users than the number of antennas can be served at a time.
Based on the discussion of FIGS. 1-3 (described above), and an understanding that users in the system may be in constant movement, conventional cluster controllers 120 have often been designed to obtain CSIT for each user equipment 145 served by the cluster, prior to selecting subsets of users for scheduling transmissions. CSIT characterizes the state of all links between each base station 110 and the respective user equipment 145 of the cluster. Specifically, CSIT may include both large-scale fading coefficient (i.e., path-loss coefficients), which are constant across collocated users, and small-scale fading coefficients (i.e., Rayleigh fading coefficients), which possess time-variations that are much faster than the path-loss and change within collocated user groups (it should be understood that the number of small-scale fading coefficients is equal to the number of receiving and transmitting antennas at the base station). By first obtaining CSIT, the central scheduling unit 125 of the cluster may select subsets of approximately orthogonal users (with cardinality not larger than the number of jointly coordinated transmit antenna) for transmission at a same frequency and time. However, for systems with a large number of users per cluster, the cost of first obtaining CSIT feedback for all user equipment (prior to selecting subsets of users) becomes prohibitive.